Analysis of an age-structured dengue model with multiple strains and cross immunity

Dengue fever is a typical mosquito-borne infectious disease, and four strains of it are currently found. Clinical medical research has shown that the infected person can provide life-long immunity against the strain after recovering from infection with one strain, but only provide partial and temporary immunity against other strains. On the basis of the complexity of transmission and the diversity of pathogens, in this paper, a multi-strain dengue transmission model with latency age and cross immunity age is proposed. We discuss the well-posedness of this model and give the terms of the basic reproduction number R-0 = max{R-1, R-2}, where R-i is the basic reproduction number of strain i (i = 1, 2). Particularly, we obtain that the model always has a unique disease-free equilibrium P-0 which is locally stable for R-0 < 1. And same time, an explicit condition of the global asymptotic stability of P-0 is obtained by constructing a suitable Lyapunov functional. Furthermore, we also shown that if R-i > 1, the strain-i dominant equilibrium P-i is locally stable for R-j < R-i* (i, j = 1, 2, i not equal j). Additionally, the threshold criteria on the uniformly persistence, the existence and global asymptotically stability of coexistence equilibrium are also obtained. Finally, these theoretical results and interesting conclusions are illustrated with some numerical simulations.